Joint asymptotic distributions of kernel estimators for a finite number of quantiles under strong mixing high-frequency data

Quantiles play an important role in financial and statistical fields, while high-frequency data are prevalent at present. In this paper, we study joint asymptotic distributions of kernel estimators for a finite number of quantiles under strong mixing high-frequency data. We show that the joint distributions are asymptotically multivariate normal distributions by using the blockwise technique. We also obtain the confidence intervals for the difference of any two quantiles based on this result. In addition, results of a simulation study on the performance of the confidence intervals under finite samples are reported, while an empirical analysis for the applications of the theoretical results is presented.